The control of static VAR compensators and other high power converter equipment requires the accurate measurement of the amplitude of the fundamental component of the line voltage. Two techniques have been used to this effect, but each has inherent drawbacks.
The first approach consists in performing fullwave rectification of each of the 3-phase input voltages, and summing the three rectified signals to produce an output signal, the DC component of which is the desired fundamental amplitude. Precision rectifiers are necessary in order to prevent errors in the output due to diode drops. Nevertheless, the output is not pure DC and it may contain harmonic ripple components primarily at the following frequencies:
1. At six times the fundamental frequency: This harmonic component is inherently present, unless 12-phase rectification is used which, then, will produce a twelve times ripple. PA1 2. At twice the fundamental frequency: This component is present when the input voltages are balanced. PA1 3. At the fundamental frequency: This component is present then one or more o the input voltages contain a DC component. PA1 1. Underclamped transient responses. PA1 2. Difficulty to tune, since the fundamental frequency changes, whereupon, complex tracking filters are necessary to cope with the problem. PA1 3. Reduced bandwidth. PA1 4. A prohibitive number of notch filters which have become necessary in order to attenuate all cyclic ripple. The remaining residual ripple affects the regulation process by precluding the effective use of signal differentiation in the control loop.
Moreover, the presence of any harmonic signal in the input voltages will result in some ripple at the output. Ripple has been a problem conventionally corrected by using notch filters essentially at the above three frequencies. However, these introduce further drawbacks:
In addition, the use of rectification has proved to be inaccurate when the input signals contain more than a given level of second harmonic. To cope with this, notch filters on the AC side tuned at twice the fundamental frequency have been used, but this has an adverse impact on the system response.
The second approach to an accurate measurement of the amplitude of the fundamental component is the "sum-of-squares" method. Here, each of the three input voltages is squared and the three squared signals are summed. The square-root of the sum will yield a DC signal proportional to the input fundamental amplitude. The primary drawback here is that this method is valid only without the presence of any level of harmonic distortion component on the input. Otherwise it would result in an inaccurate fundamental amplitude determination.